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A triangle has sides A, B, and C. Sides A and B are of lengths #5# and #2#, respectively, and the angle between A and B is #(7pi)/12 #. What is the length of side C?

Answer 1

Madelyn Adams

#c ~~ 5.85#

Given:

#a = 5# #b = 2# #/_C = (7pi)/12#

The Law of Cosines is:

#c^2 = a^2 + b^2 - 2(a)(b)cos(C)#

#c^2 = 5^2 + 2^2 - 2(5)(2)cos((7pi)/12)#

#c ~~ 5.85#

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Answer 2

Charles Autterson

Using the law of cosines, the length of side C (c) can be calculated using the formula:

c = √(a^2 + b^2 - 2ab cos(C))

Where: a = length of side A b = length of side B C = angle between sides A and B

Given: a = 5 b = 2 C = (7π)/12

Plugging in the values:

c = √(5^2 + 2^2 - 2 * 5 * 2 * cos((7π)/12))

c ≈ √(25 + 4 - 20cos((7π)/12))

Now, compute the value of cos((7π)/12):

cos((7π)/12) ≈ -0.5176

Substitute this value into the equation:

c ≈ √(25 + 4 - 20 * (-0.5176))

c ≈ √(25 + 4 + 10.352)

c ≈ √39.352

c ≈ 6.276

Therefore, the length of side C is approximately 6.276.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.